BivLaplaceRL is an R package for bivariate Laplace transforms, stochastic ordering concepts, and entropy measures in reliability analysis. It consolidates the methods from three research publications into a single, CRAN-ready package.
Bivariate Laplace transforms of residual lives — closed-form Gumbel results, general numerical integration, nonparametric estimation, and NBUHR/NWUHR aging class characterisation.
BLt-Rrl framework: reversed hazard gradient, reversed mean residual life, and closed-form transforms for FGM and bivariate power distributions.
Residual entropy generating function (REGF) — a dynamic generalisation of Golomb’s information generating function, with nonparametric estimation and Monte-Carlo simulation.
Seven bivariate stochastic order checks: BLt-rl, BLt-Rrl, weak hazard rate, MRL, relative MRL, reversed hazard rate, and reversed MRL orders.
| Paper | Journal | Authors |
|---|---|---|
| Bivariate Laplace transform of residual lives and their properties | Communications in Statistics — Theory and Methods (2022) | Jayalekshmi S., Rajesh G., Nair N.U. |
| Bivariate Laplace transform order and ordering of reversed residual lives | Int. J. Reliability, Quality and Safety Engineering | Jayalekshmi S., Rajesh G. |
| On residual entropy generating function | Journal of the Indian Statistical Association 62(1):81–93 (2024) | Smitha S., Rajesh G., Jayalekshmi S. |
dgumbel_biv,
sgumbel_biv, rgumbel_biv,
pgumbel_biv)dfgm_biv,
pfgm_biv, sfgm_biv,
rfgm_biv)dbivpower,
pbivpower, sbivpower,
rbivpower)sschur_biv,
rschur_biv)blt_residual() — numerical computation for any survival
functionblt_residual_gumbel() — closed-form for Gumbel
distributionbiv_hazard_gradient() — bivariate hazard gradientbiv_mean_residual() — bivariate mean residual lifenbuhr_test() — NBUHR/NWUHR aging class testnp_blt_residual() — nonparametric estimatorsim_blt_residual() — Monte-Carlo simulation studyblt_reversed() — for any joint CDFblt_reversed_fgm() — closed form for FGMblt_reversed_power() — for bivariate power
distributionbiv_rhazard_gradient() — reversed hazard gradientbiv_rmrl() — reversed mean residual lifeblt_order_residual() — BLt-rl orderblt_order_reversed() — BLt-Rrl orderbiv_whr_order() — weak bivariate hazard rate orderbiv_wmrl_order() — weak bivariate MRL orderbiv_brlmr_order() — bivariate relative MRL orderbiv_wrhr_order() — weak bivariate reversed hazard rate
orderbiv_wrmrl_order() — weak bivariate reversed MRL
ordershannon_entropy() — Shannon differential entropyinfo_gen_function() — Golomb information generating
functionresidual_entropy() — dynamic residual entropy (Ebrahimi
& Pellerey 1995)residual_info_gen() — residual entropy generating
function (REGF)regf_profile() — REGF profile over αregf_characterise() — distribution characterisation via
REGFnp_residual_info_gen() — nonparametric REGF
estimatorsim_regf() — Monte-Carlo simulation for REGF
estimatorplot_blt_residual(), plot_blt_reversed(),
plot_regf()# Install from CRAN
install.packages("BivLaplaceRL")# Development version from GitHub
# install.packages("devtools")
devtools::install_github("itsmdivakaran/BivLaplaceRL")library(BivLaplaceRL)
# 1. Simulate from Gumbel bivariate exponential
set.seed(42)
dat <- rgumbel_biv(500, k1 = 1, k2 = 1, theta = 0.5)
# 2. Nonparametric estimate of BLT of residual lives
np_blt_residual(dat, s1 = 1, s2 = 1, t1 = 0.3, t2 = 0.3)
# 3. Compare with closed-form
blt_residual_gumbel(s1 = 1, s2 = 1, t1 = 0.3, t2 = 0.3, k1 = 1, k2 = 1, theta = 0.5)
# 4. Check weak bivariate hazard rate order
sX <- function(x1, x2) sgumbel_biv(x1, x2, k1 = 2, k2 = 2)
sY <- function(x1, x2) sgumbel_biv(x1, x2, k1 = 1, k2 = 1)
biv_whr_order(sX, sY)$order_holds
# 5. Residual Entropy Generating Function
f <- function(x) dexp(x, rate = 1)
Fb <- function(x) pexp(x, rate = 1, lower.tail = FALSE)
residual_info_gen(f, Fb, alpha = 2, t = 0.5)Mahesh Divakaran (maintainer) Research Scholar, Amity School of Applied Sciences, Amity University Lucknow imaheshdivakaran@gmail.com
S. Jayalekshmi, G. Rajesh, N. Unnikrishnan Nair Department of Statistics, Cochin University of Science and Technology
Smitha S. K. E. College, Mannanam
Jayalekshmi S., Rajesh G., Nair N.U. (2022). Bivariate Laplace transform of residual lives and their properties. Communications in Statistics — Theory and Methods. https://doi.org/10.1080/03610926.2022.2085874
Jayalekshmi S., Rajesh G. Bivariate Laplace transform order and ordering of reversed residual lives. International Journal of Reliability, Quality and Safety Engineering.
Smitha S., Rajesh G., Jayalekshmi S. (2024). On residual entropy generating function. Journal of the Indian Statistical Association, 62(1), 81–93.
GPL-3 © 2024 Mahesh Divakaran